This paper reports on a simple novel concept of addressing the problem of underdetermination in linear spectral unmixing. Most conventional unmixing techniques fix the number of end-members on the dimensionality of the data, and none of them can derive multiple (2⁺) end-members from a single band. The concept overcomes the two limitations. Further, the concept creates a processing environment that allows any pixel to be unmixed without any sort of restrictions (e.g., minimum determinable fraction), impracticalities (e.g., negative fractions), or trade-offs (e.g., either positivity or unity sum) that may be associated with conventional unmixing techniques. The proposed mix-unmix concept is used to generate fraction images of four spectral classes from Landsat 7 ETM+data (aggregately resampled to 240 m) first principal component only. The correlation coefficients of the mix-unmix image fractions versus reference image fractions of the four end-members are 0.88, 0.80, 0.67, and 0.78.